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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Differential forms on quotients
by reductive group actions


Author: Michel Brion
Journal: Proc. Amer. Math. Soc. 126 (1998), 2535-2539
MSC (1991): Primary 14L30, 22E99
MathSciNet review: 1451789
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Abstract: Let $X$ be a smooth affine algebraic variety where a reductive algebraic group $G$ acts with a smooth quotient space $Y=X//G$. We show that the algebraic differential forms on $X$ which are pull-backs of forms on $Y$ are exactly the $G$-invariant horizontal differential forms on $X$.


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Additional Information

Michel Brion
Affiliation: Institut Fourier, B. P. 74, 38402 Saint-Martin d’Hères Cedex, France
Email: mbrion@fourier.ujf-grenoble.fr

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04320-2
PII: S 0002-9939(98)04320-2
Received by editor(s): October 25, 1996
Received by editor(s) in revised form: January 29, 1997
Communicated by: Roe Goodman
Article copyright: © Copyright 1998 American Mathematical Society